A singular perturbation limit of diffused interface energy with a fixed contact angle condition

Preprint English OPEN
Kagaya, Takashi; Tonegawa, Yoshihiro;
(2016)

We study a general asymptotic behavior of critical points of a diffused interface energy with a fixed contact angle condition defined on a domain $\Omega \subset \mathbb{R}^n$. We show that the limit varifold derived from the diffused energy satisfies a generalized cont... View more
  • References (17)
    17 references, page 1 of 2

    [1] W. Allard, On the first variation of a varifold, Ann. of Math. 95 (1975), pp 417-491.

    [2] J. W. Cahn, Critical point wetting, J. Chem. Phys. 66 (1977), pp 3667-3672.

    [3] J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system I. Inter facial free energy, J. Chem. Phys. 28 (1958), pp 258-267.

    [4] L. C. Evans and R. F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Math., CRC Press (1992).

    [5] J. Hutchinson and Y. Tonegawa, Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory, Calc. Var. Partial Differential Equations 10 (2000), no. 1, pp49-84.

    [6] T. Ilmanen, Convergence of the Allen-Chan equation to Brakke's motion by mean curvature, J. Diff. Geom. 38 (1993), no. 2, pp 417-461.

    [7] T. Kagaya and Y. Tonegawa, A fixed contact angle for varifolds, arXiv:1606.00164.

    [8] A. Malchiodi and J. Wei, Boundary interface for the Allen-Cahn equation, J. Fixed Point Theory Appl. 1 (2007), pp 305-336.

    [9] A. Malchiodi, W.-M. Ni and J. Wei, Boundary-clustered interface for the Allen-Cahn equation, Pacific J. Math. 229 (2007), pp 447-468.

    [10] M. Mizuno and Y. Tonegawa, Convergence of the Allen-Chan equation with Neumann boundary conditions, SIAM Journal on Mathematical Analysis 47 (2015), no. 3, pp 1906-1932.

  • Metrics
Share - Bookmark